This invention relates to the topical ophthalmic use of antibiotics in combination with anti-inflammatory steroids when indicated for treatment of ophthalmic infections and attendant inflammation. Such combinations or formulations are available in the ophthalmic art. However, there are concerns and expressed reservations in the ophthalmic community about the safety and efficacy of such prior art combinations. There is, moreover a long felt need for an effective and safe topical ophthalmic pharmaceutical composition of a potent steroid and a broad spectrum antibiotic which, when administered to the eye when indicated for bacterial infection or as a prophylactic after ophthalmic trauma and injury, will not, as a possible expression of the steroid component, inhibit the activity of the antibiotic or interfere width normal wound healing, but at the same time will control inflammation. Unexpectedly it has been discovered that the broad spectrum aminoglycoside antibiotic tobramycin in combination with the potent steroid dexamethasone meets these criteria.